Transforming (morphing) one object's shape into another's
Morphing objects with different vertex count is impossible AFAIK with the blender tools, unless you use a scripting. Here's a temporary solution though. It uses a to sphere tool. 


I have three objects here with a different vertex count. I'll use a sphere as a midpoint for all transformations.


Add a shape key (Key 1) and set its value to 1.000. Enter Edit Mode and use To Sphere tool (Shift+Alt+S,1). Then hit Ctrl+V-->Smooth Vertex. Hold Shift+R to repeat it (set smoothing value to 1.000 in a Tool Shelf) unless the vertices are relaxed. Then repeat the to sphere operation.


Do the same with the other objects (every one should transform to the sphere of an equal size). Finally keyframe the shape keys values and visibility of the objects on a timeline.